1. Statement of the Technical Field
The invention concerns communications systems. More particularly, the invention concerns systems and methods for improving symbol estimation in spread spectrum communications.
2. Description of the Related Art
There are many types of communications systems known in the art, such as multiple access communications systems, low probability of intercept/low probability of detection (LPI/LPD) communications systems and spread spectrum communications systems. Many of these systems depend on equal duration symbols, and/or equal energy spreading sequences. Other systems induce exploitable correlations via square-wave pulse shaping to improve reception. Non-square wave spreading sequences (including chaotic spreading sequences) have also been employed but require significantly more computational power to synchronize due to the non-stationary temporal distribution of signal energy. As used herein, non-stationary refers to a sequence or signal that fails to be wide sense stationary, which is approximately equal to having a constant expected energy or value during any arbitrarily chosen equal-length time interval. Most spread spectrum communication systems based on equal energy spreading sequences may be treated as stationary, while non-equal energy based spreading sequences (such as a chaotic spreading sequence) approximate stationary systems in their long-term behavior only; bit error rates (BER) and other symbol-duration dynamics are degraded when models and algorithms treating the non-stationary spreading sequence as stationary are employed. However, models that deal with stationary signals are much easier to construct and use.
Communication signals employing non-equal energy spreading sequences are typically more secure and robust to interferers, especially those that approach the maximal entropy signals considered ideal for channel capacity transmission of energy in a flat AWGN channel. A primary example of a non-stationary spreading sequence that has applicability in spread spectrum communications is a chaotic spreading sequence. As described herein, a chaotic spreading sequence consists of a sequence of numbers having values that appear to have unpredictable transitions characteristics following that of a mathematically chaotic evolution and near ideal statistical properties, yet follow a well-defined deterministic evolution.
In some cases, communication systems use a form of amplitude modulation, such as quadrature amplitude modulation (QAM) for transmitting communication signals. QAM is a modulation scheme in which two sinusoidal carriers, one exactly 90 degrees out of phase with respect to the other, are used to transmit data over a given physical channel. Because the orthogonal carriers occupy the same frequency band and differ by a 90 degree phase shift, each can be modulated, transmitted over the same frequency band, and separated by demodulation at the receiver. Thus, each symbol can be represented by a particular combination of phase shift and amplitude shift in two orthogonal dimensions, leading to higher user data capacities in the same channel. However, as the number of symbols represented by the sinusoidal carriers is increased without increasing the power envelope for the signals, the Hamming distance between symbols is decreased. This typically results in symbols that are more susceptible to noise and other corruptions, leading to higher bit error rates and less reliable delivery of data. In particular, the use of a non-stationary spreading sequence to spread an amplitude modulated data symbol is susceptible some level of degradation caused by natural variations in the symbol energy that change dynamically on a symbol by symbol basis. Combining the capabilities of the higher capacity data modulations with the susceptibility of a non-stationary spreading sequence to symbol energy variations, there is a need for methods or mechanisms to normalize the non-stationary symbol energy in order to improve data reception capabilities.